LINEAR VERSUS LOGARITHMIC AVERAGING
Abstract
Consider n data samples (x1,...,xn) such that 0 < L = or < xi = or < U < infinity. Let K = U/L; then it is shown that independent of n a lower bound on the ratio of the geometric mean to the arithmetic mean of the data samples is given by (ln K/(K -1))K to the power ((1/ln K) - 1/(K-1)). This bound is useful in acoustic signal processing since it limits the amount of deviation that can be attributed to averaging logarithms vice taking the logarithm of the average of data samples. Both methods are currently in use at facilities specializing in the processing of acoustic data. For a K of 10 dB, for example, the geometric mean is less than 1.5 dB below the arithmetic mean.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jun 01, 1967
- Accession Number
- AD0657404
Entities
People
- David W Taylor
- Henry Cox